[RASMB] Help! No model fits my sedimentation eq data

[Guinevere A. Murphy]

Dear RASMB,

I am (a novice at) working with equilibrium sedimentation data for a 16.9
kDa protein (E280=2680 /M cm), collected at three concentrations of 56, 94
and 136 microMolar. I collected data at four speeds, 20, 25, 30 and 35
krpm. The protein is a long dimeric coiled coil, so I expect to have a
monomer-dimer equilibrium. There is a possibility of higher order
structure, so a mono-dimer-tetramer equilibrium would not be out of the
question, either.

I have been analyzing the data using MacNonlin. For the two 20K data sets
I collected, I can locally fit the lowest 56 micromolar data to a single
ideal component model, (initial guesses: sigma=1.8 (dimer), deltaY=3E-3,
and lnA=-2.6) I get nice random residuals, and a sqrt variance of ~4E-3.
The fitted sigma corresponds to a 29 kDa component (between the expected
16.9 and 33.8 monomer and dimer MWs).

If I fit to a monomer-dimer equilibrium for this data set, I also get
reasonable sqrt variances (4E-3) and nice random-looking residuals, and I
get a Kd of 28 microMolar (using the 1/Ka, after converting the Ka from
absorbance units with the formula Ka(M)=[Ka(AU)*E(monomer)*(1.2cm
path)]/2). I view this high number with skepticism, both because it is
pretty high, for what I might expect, and because I am only fitting one
concentration and speed.

So, I would like to add in other data sets, however I find that I am
unable to fit any of the other data to a reasonable model in a manner
which produces anything like random residuals, and the sqrt variances are
all high (well above 1E-2). This is true for fitting to single ideal
component, monomer-dimer, monomer-trimer, dimer-tetramer and many others
that are not as obvious.

There are two observations regarding local fitting of one of the data sets
that I am having trouble with that I think might be suggesting nonspecific
aggregation of the protein at higher concentrations, and later time points
(20K was collected first):

a.) If I vary B, the second virial coefficient, I do get a random
distribution of residuals, and sqrt variance of 3E-3, but the value B gets
fitted to is -0.57. I know positive values of B suggest nonideality, but
does negative mean it is ideal and just isn't being fitted to the proper
model?

b.) If I set sigma=1.9 (for dimer) and don't vary it, and then vary
N2(init guess at 2, so init guess is for dimer-tetramer equilibrium) lnK2
(init guess at 8), lnA (init guess -3), delY (init guess 7E-2), then I get
the most reasonable fit to the data I've seen, and the residuals are not
totally random, but more dispersed and random than any other model, with a
sqrt variance of 6E-3.  However, the fitted parameters go to N2=17.5, and
lnK2=9.5!

This result suggests to me that either I've got one heck of a large
oligomer, or there is nonspecific aggregation occurring.

Would anyone have insight into this this difficult-to-fit data? And if it
is likely nonspecific aggregation, is there a definitive diagnostic that
would show that with the data I already have?

Thanks very much for taking the time to read this, and for your
suggestions and comments!

Gwen Murphy

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Guinevere A. Murphy		    Chemistry and Biochemistry Department
murphyg at ucsu.colorado.edu	    The University of Colorado at Boulder
http://ucsu.colorado.edu/~murphyg
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~